Simultaneous Spatial and Spectral Low-Rank Representation of Hyperspectral Images for Classification

Arising from various environmental and atmos- pheric conditions and sensor interference, spectral variations are inevitable during hyperspectral remote sensing, which degrade the subsequent hyperspectral image analysis significantly. In this paper, we propose simultaneous spatial and spectral low-rank representation (S3LRR) that can effectively suppress the within-class spectral variations for classification purposes. The S3LRR recovers an intrinsic component with the same dimension as the original image, in which both spatial and spectral low-rank priors are adopted to regularize the intrinsic component simultaneously and compensate to each other, together with robust modeling of spectral variations. Compared with existing methods that explore only the spectral low-rank prior, the novel spatial low-rank prior (i.e., low-rank prior in band-wise) can take the spatial structure information of hyperspectral images into account, which has demonstrated to be very useful. Technically, we formulate S3LRR as a constrained convex optimization problem, and solve it using the efficient inexact augmented Lagrangian multiplier method. The resulting intrinsic component is less interfered by within-class spectral variations, and more discriminatory to offer higher classification accuracy. Comprehensive experiments on benchmark data sets demonstrate that the proposed S3LRR improves classification accuracy significantly, which outperforms state-of-the-art methods.